Static and dynamical spin correlations of the S = 1 2 random-bond antiferromagnetic Heisenberg model on the triangular and kagome lattices

Abstract

Inspired by the recent theoretical suggestion that the random-bond $S=1/2$ antiferromagnetic Heisenberg model on the triangular and the kagome lattices might exhibit a randomness-induced quantum spin liquid (QSL) behavior when the strength of the randomness exceeds a critical value, and that this ``random-singlet state'' might be relevant to the QSL behaviors experimentally observed in triangular organic salts $\ensuremath{\kappa}\text{\ensuremath{-}}{(\mathrm{ET})}_{2}{\mathrm{Cu}}_{2}{(\mathrm{CN})}_{3}\phantom{\rule{4pt}{0ex}}\mathrm{and}\phantom{\rule{4pt}{0ex}}{\mathrm{EtMe}}_{3}\mathrm{Sb}{[\mathrm{Pd}{(\mathrm{dmit})}_{2}]}_{2}$ and in kagome herbertsmithite ${\mathrm{ZnCu}}_{3}{(\mathrm{OH})}_{6}{\mathrm{Cl}}_{2}$, we further investigate the nature of the static and the dynamical spin correlations of these models. We compute the static and the dynamical spin structure factors, $S(\mathbf{q})$ and $S(\mathbf{q},\ensuremath{\omega})$, by means of an exact diagonalization method. In both triangular and kagome models, the computed $S(\mathbf{q},\ensuremath{\omega})$ in the random-singlet state depends on the wave vector $\mathbf{q}$ only weakly, robustly exhibiting gapless behaviors accompanied by the broad distribution extending to higher energy $\ensuremath{\omega}$. Especially in the strongly random kagome model, $S(\mathbf{q},\ensuremath{\omega})$ hardly depends on $\mathbf{q}$, and exhibits an almost flat distribution for a wide range of $\ensuremath{\omega}$, together with a $\ensuremath{\omega}=0$ peak. These features agree semiquantitatively with the recent neutron-scattering data on a single-crystal herbertsmithite. Furthermore, the computed magnetization curve agrees almost quantitatively with the experimental one recently measured on a single-crystal herbertsmithite. These results suggest that the QSL state observed in herbertsmithite might indeed be the randomness-induced QSL state, i.e., the random-singlet state.